【作者】 刘玉兰；

【导师】 葛庆平；

【作者基本信息】 首都师范大学 ， 计算机应用技术， 2005， 硕士

【摘要】 光栅图像的矢量化主要由图像分割及矢量获取两部分组成。通过图像分割得到目标图像的边缘线或骨架线,并以离散点序列形式表示出来。矢量获取则将这些点序列转换成首尾相连的曲线段或具有一定逻辑关系的图元对象,如圆弧、直线、椭圆弧等。矢量获取是光栅图像矢量化的关键部分,也是本文的研究重点,本文在后面提到的矢量化算法,都是指矢量获取算法。衡量一个矢量化算法效果好坏的根本标准是曲线段或图元对象与原始点序列间的误差大小及其相对原始数据的压缩率。从理论上来讲,误差越小,压缩率越大,则矢量化的效果越好。但这种高压缩率和低误差往往是以大量的计算为代价换来的,如在某些最优化算法中,通过不断排除不满足要求的解,最后得到具有最优性能的解,此过程需要进行大量的计算,不符合实际生产中高效率的要求。在实际的生产应用中,往往是一定的精度和压缩率就能满足生产需要,因此应当根据具体的要求选择合适的矢量化算法,避免不必要的计算。 本文研究的课题背景是鞋样设计和扩缩CAD系统(在后面简称为鞋样系统)。该系统将放有鞋样的背景图片由数码相机输入到计算机内,经图像分割后得到鞋样轮廓的数字点序列表示。由于这些离散的点序列数据量太大且存在大量细小的毛刺,不利于设计人员对其进行编辑和利用切割机进行切割,因此需转换成矢量图形。根据实际需要,本系统中拟合曲线与鞋样边缘的最大误差不能超过2毫米(对应屏幕中的5个像素点),且矢量图在保持原始边缘特征的基础上能对原始数据能进行较大的压缩。因此,本文在研究现有算法的基础上提出了一种分段递归拟合矢量化算法。该算法首先通过计算曲率提取尖点将轮廓进行分段,然后对每两个尖点之间的曲线段用抛物样条曲线进行递归拟合。在提取尖点时又提出了一种间接的方法,大大简化了曲率的计算。最后实验证明,递归方法能通过中止条件很好的控制拟合的精度和压缩率,在满足精度要求的同时减少不必要的计算。因此该算法能满足鞋样系统的要求。更多还原

【Abstract】 The vectorization of raster images including two steps: image division and vector getting. Through image division we get the edge or framework of a target in form of point series. Vector getting fits the point series with curves such as arcs, lines and ellipse arcs etc. These curves are joining end to end. Vector getting is a key step in the process of raster image vectorization and is the most important part of this article. In the following part of this article vectorization is equal to vector getting. A good vectorization algorithm can not only fit the point series with little error, but also can reduce the data in large amount. In theory, the less fitting error and bigger compress rate, the better a vectorization algorithm is. But little fitting error and big compress rate always take a large amount of calculating, such as in some optimum algorithms, to find the best result always need many times of iterative calculating. In practice, certain fitting error and compress rate can satisfy the demand, so we should choose a suitable algorithm to avoid unnecessary calculating.The background of this article is the shoe pattern design and enlarge and constrict system (shoe pattern system in abstract). In this system, photos of shoe patterns are transmitted to computer from digital cameras. After image division, we get the outlines of shoe patterns in form of point series. The amount of points of a shoe pattern is very large and there are many noises among these points, these make us difficult to enlarge or constrict the shoe pattern, so these point series should be turned into vectors before a shoe pattern is operated in computer. Fitting error of vectorization should be less than 2mm(5 pixels in the digital image) in this system, and a certain compress rate should be get in condition of keep the feature of the shoe pattern outline. In this article, we present a recursive vectorization algorithm based on the existing ones. This algorithm first separate the outline with cusps and a new way of getting cusp points is presented. This new cusp getting way has a less amount of calculating compared with general ways. After separating, algebraic curves was used to fit digital curves between every two cusps in recursive. The experiment of this algorithm shows that recursive algorithm can control the fitting error and compressrate very well through ending condition, without unnecessary calculating, so this algorithm can satisfy the demand of the shoe pattern system.更多还原